Calphad coupled phase-field model with mechano-chemical contributions and its application to rafting of γ′ in CMSX-4

A novel Calphad coupled mechano-chemical phase-field model is presented which in addition to chemo-elastic contributions to the driving force further includes mechano-chemical effects on diffusion (stress-driven diffusion), equilibrium compositions and driving force. These effects have their origin in the concentration dependency of the eigenstrains and can significantly influence the phase transformation kinetics, especially in Ni-based superalloys where the different dissolved elements have strongly different partial molar volumes. In this paper, all mechano-chemical contributions to diffusion, equilibrium concentrations and driving force are derived starting from a free energy functional. In order to use the model in conjunction with Calphad databases, elastic effects are incorporated in an efficient and consistent way by a posteriori treatment of the chemical quasi-equilibrium data. The new model is first applied to evaluate the 3D-equilibrium shape of a single gamma'-particle in a binary Ni-Al and a ternary Ni-Al-Mo alloy and then for the simulation of Ostwald ripening and rafting of the multicomponent CMSX-4 alloy. Results from simulations with and without consideration of the mechano-chemical contributions are compared. It is shown that, especially in case of the ternary and multicomponent alloys, the mechano-chemical effects on the equilibrium shapes of the gamma'-particles and on interface kinetics are considerable and cannot be neglected. Moreover, different standard homogenization assumptions for stresses and strains inside the diffuse interface region (Voigt-Taylor, Khachaturyan, Reuss-Sachs) have been systematically compared and analyzed using an extended quasi-equilibrium approach, leading to a new evaluation of their applicability in the context of mechano-chemical coupling.